Agricultural Systems xxx (2013) xxx–xxx

Contents lists available at ScienceDirect

Agricultural Systems

journal homepage: www.elsevier .com/locate /agsy

Operational planning of herbicide-based weed management

0308-521X/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.agsy.2013.07.006

⇑ Corresponding author. Address: Departamento de Agronomía, UniversidadNacional del Sur, Av. Colón 80, Bahía Blanca 8000, Argentina. Tel.: +54 2914595102; fax: +54 291 4595127.

E-mail addresses: mlodovichi@criba.edu.ar (M.V. Lodovichi), ablanco@plapiqui.edu.ar (A.M. Blanco), gchantre@criba.edu.ar (G.R. Chantre), abandoni@plapiqui.edu.ar (J.A. Bandoni), cesabbat@criba.edu.ar (M.R. Sabbatini),mvigna@bordenave.inta.gov.ar (M. Vigna), rllopez@bordenave.inta.gov.ar(R. López), ramongigon@yahoo.com.ar (R. Gigón).

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning of herbicide-based weed management. Agr. Syst. (2013), http://dx.d10.1016/j.agsy.2013.07.006

Mariela V. Lodovichi a,⇑, Aníbal M. Blanco b, Guillermo R. Chantre a, J. Alberto Bandoni b,Mario R. Sabbatini a, Mario Vigna c, Ricardo López c, Ramón Gigón c

a Departamento de Agronomía/CERZOS, Universidad Nacional del Sur/CONICET, Bahía Blanca 8000, Buenos Aires, Argentinab Planta Piloto de Ingeniería Química, Universidad Nacional del Sur/CONICET, Bahía Blanca 8000, Buenos Aires, Argentinac EEA INTA Bordenave, Bordenave 8187, Buenos Aires, Argentina

a r t i c l e i n f o a b s t r a c t

Article history:Received 20 December 2012Received in revised form 24 May 2013Accepted 26 July 2013Available online xxxx

Keywords:Weed managementPlanning modelHerbicide applicationsEnvironmental impactWinter wheatWild oat

Weeds cause crop yield loss due to competition, interfere with agricultural activities and reduce grainquality due to seed contamination. Among the numerous methods for weed control, the use of herbicidesis the most common practice. Nowadays, the optimization of herbicide application is pursued to reducethe environmental impact, delay the appearance of herbicide-resistant weed populations, and improvethe cost/benefit ratio of the agronomic business. This work proposes an operational planning model,aimed at calculating the optimal application times of herbicides in no-tillage systems within a growingseason in order to maximize the economic benefit of the activity while rationalizing the intensity of theapplications with respect to expert-knowledge-based recommendations. The model can decide on herbi-cide applications on a daily basis, consistent with timing of agricultural activities, and provides an explicitquantification of the environmental impact as an external cost. The proposed approach was tested on awinter wheat (Triticum aestivum)–wild oat (Avena fatua) system, typical of the semiarid region of Argen-tina. In all the studied scenarios at least two pre-sowing applications of non-selective herbicides wererequired to effectively control early emerging weed seedlings. Additional pre-sowing and post-emer-gence applications were also advised in cases when competitive pressure was significant.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Weed control in crops is mainly based on the use of herbicidesbecause they are efficient and easily applied. However, nowadays,attempts are made to minimize the use of chemicals in order tomitigate environmental impact and to avoid the appearance of her-bicide-resistant weed populations (Pannell et al., 2004; Parsonset al., 2009). The optimization of weed control is largely recognizedto be a challenging and information demanding task. Wiles et al.(1996) consider that a decision maker needs information aboutweed emergence patterns, crops competitive ability, impact ofweeds on crop yield and quality, and on available managementoptions.

In order to integrate the available information and systemati-cally explore weed control options, several model-based decisionsupport systems (DSS) have been developed in recent years(Table 1).

Since weeds are adapted to specific agro-ecological conditions,the DSS are not supposed to be used beyond their design scopewithout proper adjustments. Therefore, in all cases the studiedweed/crop system is reported together with the country (or regionwithin a country) of origin (Table 1). Moreover, major modelingcomponents, classified as climatic, biological and economic, arealso identified. The climatic component makes reference to an ex-plicit use of weather data, while the biological component reflectsthe quantitative modeling of some of the most important eco-physiological sub-processes (emergence, seedling survival, seedproduction, etc.). This component is further classified as empiricalor mechanistic, recognizing that the mechanistic approach makesuse, in general, of some amount of empirical information.

Most DSS are devoted to typical annual weeds in wheat basedrotations (Cousens et al., 1986; Doyle et al., 1986; Berti et al.,2003; Pannell et al., 2004; Parsons et al., 2009), but other crops,such as soybean and sugar beet, have also been modeled (Bertiand Zanin, 1997; De Buck et al., 1999; Rydahl, 2004). Most systemswere also designed in European countries (Cousens et al., 1986;González-Andújar and Fernández-Quintanilla, 1991, 2004; Bertiand Zanin, 1997; Falconer and Hodge, 2001; Berti et al., 2003; Col-bach et al., 2007; Parsons et al., 2009; Torra et al., 2010). However,it is evident that the automation of weed control management is ofworldwide interest since there are also examples from Australia(Pannell et al., 2004), Africa (Mullen et al., 2003) and America

oi.org/

Table 1Model based weed management DSSs.

Reference/denomination

Weed/crop Country ofdevelopment

Model components Evaluation approach Scope Environmentalimpactd

Climatica Biologicalb Economic Simulation Optimizationc Operational Tactical/strategic

Empirical Mechanistic

Doyle et al.(1986) andCousens et al.(1986)

Alopecurusmyosuroides,Avena fatua/winter wheat

UnitedKingdom

X X X X

Sells (1995) Avena fatua,Alopecurusmyosuroides

UnitedKingdom

X X X X

Wiles et al.(1996)/GWM

General USA X X X X

Berti and Zanin(1997), Bertiet al. (2003)/GESTINF

16 weedspecies/soybean,wheat

Italy X X X X

De Buck et al.(1999)/BESTWINS

4 weedspecies/sugarbeet

TheNetherlands

X X X X X

Falconer andHodge (2001)

General UnitedKingdom

X X X X X

Mullen et al.(2003)

Striga sp. Mali X X X

González-Andújar andFernández-Quintanilla(1991, 2004)

Avena sterilis,Lolium rigidum

Spain X X X

Pannell et al.(2004)/RIM

Lolium rigidum Australia X X X X

Rydahl (2004)/CPO

75 weedspecies/11crops

Denmark X X X

Colbach et al.(2007)/ALOMYSYS

Alopecurusmyosuroides

France X X X X X

Parsons et al.(2009)/WeedManager

13 weedspecies/winter wheat

UnitedKingdom

X X X X X X

Torra et al.(2010)/PIM

Papaver rhoeas Spain X X X X

This paper Avena fatua/winter wheat

Argentina X X X X X

a Considered in a quantitative fashion (degree days, etc.).b Considers items such as: seed survival, dormancy, germination, pre-emergence growth, seedling survival, tillering, heading, flowering, and seed production.c Implements a numerical optimization algorithm to perform the search.d Considered in a quantitative fashion.

2 M.V. Lodovichi et al. / Agricultural Systems xxx (2013) xxx–xxx

(Wiles et al., 1996). Regarding the type of biological model, mostsystems are based on dynamic population balances (i.e., seedspresent in the seedbank, emerged seedlings, number of matureplants) whose flows are described through empirical parameters(González-Andújar and Fernández-Quintanilla, 1991, 2004; Pan-nell et al., 2004). In the cases where the biology is more mechanis-tically represented (Colbach et al., 2007; Parsons et al., 2009)weather data is also required.

Economic analyses are also performed in most DSS in order toevaluate the potential profit of implementing different control pro-cedures (Cousens et al., 1986; Wiles et al., 1996; Berti and Zanin,1997; Falconer and Hodge, 2001; Berti et al., 2003; Pannell et al.,2004; Parsons et al., 2009; Torra et al., 2010). Regarding the evalu-ation approach, most systems are designed to be used in a simula-tion-oriented fashion, meaning that a certain strategy is proposedand its effect on the weed–crop system is calculated (González-Andújar and Fernández-Quintanilla, 2004; Pannell et al., 2004). Inthis way, different possible scenarios can be tested and rankedaccording to their economic output. However, due to the combina-torial amount of feasible control options (chemical and non-chem-ical) on a long term time-horizon of several seasons, some DSS also

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning10.1016/j.agsy.2013.07.006

implement numerical optimization algorithms to automate thesearch (Sells, 1995; De Buck et al., 1999; Falconer and Hodge,2001; Mullen et al., 2003; Rydahl, 2004; Parsons et al., 2009).

Regarding the scope of application, the conducted research onDSS development has been basically focused on the tactical/strate-gic planning problem, which addresses the weed control decisionsover a long-term horizon of several years. In this regard, the DSSdivide the seasons into periods of biological and agronomic sense,rather than using a daily step, to perform the calculations andimplement the control operations. Finally, although all the DSSare designed to rationalize the chemical use and mitigate the envi-ronmental impact of weed control, only two models explicitly per-form some quantitative evaluation of an environmental impactrelated indicator. Specifically, in Berti and Zanin (1997) and Bertiet al. (2003) the potential contamination of groundwater is consid-ered, while in Falconer and Hodge (2001) the impact of pesticidesapplication is analyzed within a bi-objective (economic-environ-mental) optimization approach.

From the above review, it can be stated that the contributionsare basically focused on the tactical/strategic planning problem.To the best of our knowledge, no proposals related to the herbicide

of herbicide-based weed management. Agr. Syst. (2013), http://dx.doi.org/

M.V. Lodovichi et al. / Agricultural Systems xxx (2013) xxx–xxx 3

selection problem integrated with the calculation of the optimalapplication times have been presented so far. Such short-termproblem can be considered as an ‘‘operational planning’’ problemof the agricultural activity. The importance of the operational plan-ning perspective relies on the fact that if herbicide applications aremade too soon, later emergence will require additional interven-tions for effective control, incurring in additional costs and envi-ronmental impact. On the other hand, if the herbicideapplications are delayed, older weeds might survive, competingwith the crop and producing new seeds.

The main difficulty related to the operational planning of herbi-cide based weed control is that the emergence pattern of the weedis uncertain. It is well known that in order to make an efficient useof herbicides, an accurate prediction of the relative time of weedseedling emergence and density is essential (Forcella et al.,2000). It should be pointed out that an accurate estimation of weedemergence dynamics is a challenging goal since emergence onsetand magnitude depend on soil microclimatic conditions, usuallydescribed in terms of hydrothermal time accumulation, and arealso modulated by complex adaptative seed dormancy traits, asstated by Chantre et al. (2012, in press) for wild oat.

This work proposes a conceptual operational planning modelwhose main features are summarized in Table 1. The system wildoat (Avena fatua)–winter wheat (Triticum aestivum), typical of thesemiarid region of Argentina, is used as a case study. The aim isto maximize the economic benefit of the agricultural activity withexplicit consideration of the environmental impact of pesticideuse, through the selection of the proper herbicides and the corre-sponding application times in a no-tillage system along the grow-ing season.

2. Materials and methods

2.1. Crop yield loss

Crop yield loss (yL) caused by competition with a single weedspecies has been described by the rectangular hyperbola modelof Cousens (1985):

yL ¼iD

1þ iDa

ð1Þ

where D is weed density in plants m�2, parameter i is the percentyield loss per weed plant per unit area as weed density approacheszero and parameter a is the upper limit of percent yield loss as weeddensity approaches infinity. Eq. (1) assumes that all weed plantspresent in the field emerge simultaneously with the crop and com-pete with it until harvest.

As yield loss cannot be observed directly, the final yield of thecrop (y) has to be estimated as a proportion of the weed-free cropyield (ywf) in kg ha�1, through the following relation:

y ¼ ywf 1� yL

100

� �ð2Þ

Since weed seedlings do not usually emerge simultaneouslywith the crop, the final weed density is in general not adequateto calculate the actual yield loss. In fact, seedlings that emerge ear-lier in the season cause greater yield losses than those that emergelater (Cousens et al., 1987; Berti et al., 1996). Cousens et al. (1987)modified model (1) to include the relative emergence time of theweed as a parameter:

yL ¼bD

ecRT þ bDa

ð3Þ

where RT is the time interval between weed and crop emergence, bis the value of i when RT = 0 and c is the rate at which i decreases as

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning10.1016/j.agsy.2013.07.006

RT becomes larger. RT is negative if weed seedlings emerge earlierthan the crop and positive if the crop emerges first.

This approach still considers that all weed seedlings emergesimultaneously. However, in nature field emergence patterns aremostly determined by successive cohorts that impact on crop yielddifferently depending on the relative emergence time (Berti et al.,1996). Based on Eq. (3) Berti et al. (1996) proposed the use of theconcept of ‘‘time-density equivalent’’ (TDE) to consider both, seed-ling emergence time and relative emergence, on the estimation ofcrop yield loss. For weed seedlings with a given emergence time,TDE can be defined as the density of a reference weed that emergesuniformly and competes with the crop until harvest causing thesame yield loss as that incurred by the actual weed. Early emergingweeds have a larger TDE than those emerging later. TDE of eachdaily cohort is calculated as:

TDEt ¼ D expð�cRTtÞ ð4Þ

In this work we used the concept of TDE to account for the effectof weed cohorts (i.e. seedlings emerging at different moments).TDE was calculated in a daily basis, and then integrated to obtaina global TDE. This global TDE was used instead of weed density(D) to estimate crop yield loss in Eq. (1).

2.2. Pesticide Environmental Accounting (PEA)

To account for the environmental impact of pesticides use,Leach and Mumford (2008) developed a methodology to estimatethe associated external costs. External costs include monitoringfor contamination of soil, water and food, and poisoning of humansand fauna. Such costs are usually absorbed by society and, there-fore, not taken into account in individual decision making so far.The approach by Leach and Mumford is based on the Environmen-tal Impact Quotient (EIQ) (Kovach et al., 1992). The EIQ describesthe environmental impact of a pesticide in terms of an eco-toxico-logical quotient. The EIQ is calculated for each pesticide consider-ing eight categories: toxicological effects on pesticide applicators,pickers and consumers, ground water contamination, aquatic ef-fects and toxicological effects on birds, bees and beneficial insects.

Pesticide Environmental Accounting provides the external costper kg of active ingredient of an average pesticide. This externalcost is distributed into the eight EIQ components. Each categoryis classified as having low, medium or high impact according tocorresponding EIQ values and the external cost is weighted by acoefficient of 0.5, 1.0 or 1.5 respectively. These external costs arethen adjusted for each chemical by the active ingredient concen-tration on the formulated (or commercial) product and by the fieldapplication rate for each chemical. External costs calculated byPesticide Environmental Accounting (in Euros ha�1 application�1)are based on average estimations from the United Kingdom, theUnited States of America and Germany considering the monitoringand remediation of damaged habitats and treatment of acute poi-soning (Pretty et al., 2000, 2001). To adapt this calculation toArgentina, the external costs were scaled to the Argentinean GrossDomestic Product (GDP) as a proportion of the average GDP of thereference countries according to the approach proposed in Leachand Mumford (2008). Pesticide Environmental Accounting was ap-plied to the specific case of herbicides use in sugar beet systems inLeach and Mumford (2011). For further details about PesticideEnvironmental Accounting calculation see Appendix A.

2.3. Planning model development

The developed planning model is presented below. It was builton the previously described elements and structured within theframe of a multi-period mathematical programming formulation.A one year time horizon with a daily time step was considered

of herbicide-based weed management. Agr. Syst. (2013), http://dx.doi.org/

Table 2Model indexes and variables.

Symbol Name

Indexest Time period (calendar days)h {hs,

hns}Herbicide (s: selective, ns: non-selective)

VariablesDt Weed density (plants m�2)TDEt Daily time–density equivalent (plants m�2)TDEtot Global TDE (plants m�2)Ettt Weed plants emerged at day t that survive and affect crop yield

(plants m�2)EMtt,h Weed plants emerged at day t killed by application of herbicide h

(plants m�2)bight,h Total applications of herbicide h during a period of (nsh2h � nsh1h)

daysMt Daily weed seedling mortality (plants m�2)Mtht,h Daily weed seedling mortality due to herbicide h (plants m�2)S Total weed seeds produced at the end of the season (seeds m�2)D1 Weed density corresponding to the first cohort (plants m�2)D2 Weed density corresponding to the second cohort (plants m�2)SR Total seed rain (seeds m�2)yL Crop yield loss (%)y Crop yield (kg ha�1)B Economic benefit ($ ha�1)Inc Gross income ($ ha�1)Cost Cost of herbicides purchase ($ ha�1)Ext Environmental cost of herbicide applications ($ ha�1)Cap Cost of herbicides application ($ ha�1)Rep Weed seed penalty ($ ha�1)yhthh,t Binary variable; 1 if herbicide h is applied; 0 instead

Table 3Weed and crop parameters.

Symbol Name Parametervalue

Source

Et Daily weed emergence(plants m�2 day�1)

Section 2.4 Experimental stationof INTA, Bordenave

a Parameter of Eq. (1) 100 Cousens et al. (1987)i Parameter of Eq. (1) 0.75 Cousens et al. (1987)c Parameter of Eq. (4) 0.119 Cousens et al. (1987)Temt Day of weed emergence

(days)Section 2.3 Experimental station

of INTA Bordenaveywf Weed-free crop yield

(kg ha�1)2000 Specific knowledge

pc Crop price ($ kg�1) 0.75 Specific knowledgens Period of crop susceptibility

to herbicides (days)26 Specific knowledge

Tec Period of time from sowing tocrop emergence (days)

17 Specific knowledge

Dec Day of crop emergence (days) Section 2.3 Specific knowledgeDes Day of crop sowing (days) 152 Specific knowledgeRTt Relative time of crop–weed

emergence (days)Section 2.3 Specific knowledge

bigM Big M constant 50,000 Specific knowledgensh1h Day of beginning of weed

susceptibility to herbicide h(days)

Table 4 Specific knowledge

nsh2h Day of end of weedsusceptibility to herbicide h(days)

Table 4 Specific knowledge

PEAh External cost of oneapplication of herbicide h($ ha�1)

Table 4 Leach and Mumford(2008)

costhh Cost of herbicide h ($ ha�1) Table 4 Specific knowledges1 Maximum number of seeds

produce per weed plant bythe first cohort(seeds plant�1)

37 González-Andújarand Fernández-Quintanilla (1991)

s2 Maximum number of seedsproduce per weed plant bythe second cohort(seeds plant�1)

10 González-Andújarand Fernández-Quintanilla (1991)

b1 Ratio of s1 to the upper limitof seed production per unitarea (m2 plant�1)

0.005 González-Andújarand Fernández-Quintanilla (1991)

b2 Ratio of s2 to the upper limitof seed production per unitarea (m2 plant�1)

0.016 González-Andújarand Fernández-Quintanilla (1991)

ap Cost of one herbicideapplication ($ ha�1)

16.5 Vigna and Gigón(pers. comm)

l Proportion of lost seeds(seeds m�2)

0.54 González-Andújarand Fernández-Quintanilla (1991)

p Seed production penalty($ m2 ha�1 seed�1)

0.4897 Section 3.3

4 M.V. Lodovichi et al. / Agricultural Systems xxx (2013) xxx–xxx

for modeling purposes, in order to account for the typical agricul-tural cycle and data availability frequency. The model provides theoptimum weed control strategy by selecting which herbicide to ap-ply each period of the planning horizon. For a complete descriptionof model variables and parameters see Tables 2–4.

2.3.1. Weed density estimationThe model predicts the evolution of weed density during the

planning horizon. The number of plants per square meter presentin the system on day t is the sum of plants in all growth stages.Density (Dt) is calculated as a plant balance among the numberof seedlings emerged on day t (Et) plus the weed density on theprevious day (Dt�1) minus the seedlings eliminated by controloperations performed on day t (Mt):

Dt ¼ Dt�1 þ Et �Mt 8 t ð5Þ

tc Day beyond which no control

operations can be performed(days)

250 Lodovichi (pers.comm)

2.3.2. Weed seedlings mortalityWeeds can be effectively controlled only if the plants are at the

appropriate growth stage. It is assumed that weed seedlings arekilled only by herbicides applications, and that all susceptible indi-viduals present in the day of the application are effectively con-trolled. It should be stressed that it is considered that herbicidesapplications control the total amount of the susceptible individu-als, not a 100% of the weed plants present the application day.Weed plants are considered susceptible to herbicide h when theirages are comprised within periods nsh1h and nsh2h. Parametersnsh1h and nsh2h are the beginning and the end of the susceptibilityperiod respectively for each specific herbicide and depend on weedseedling growth stage (see Table 4). Thus, seedlings younger thannsh1h and older than nsh2h survive to the application of the corre-sponding herbicide. In this way a ‘‘reduced efficacy’’ is representedby a shorter susceptibility period, while a larger susceptibility per-iod implies an extended control action of the herbicide.

The model calculates the number of weed seedlings killed byeach available treatment at day t (Mtht,h) as follows:

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning10.1016/j.agsy.2013.07.006

Mtht;h 6X

t�nsh2ðhÞ6t16t�nsh1ðhÞEMtt1;h þ bigMð1� yhtht;hÞ 8 t; 8 h

ð6Þ

Mtht;h PX

t�nsh2ðhÞ6t16t�nsh1ðhÞEMtt1;h � bigMð1� yhtht;hÞ 8 t; 8 h

ð7Þ

Mtht;h 6 yhtht;hbigM 8 t; 8 h ð8Þ

yhtht,h is a binary variable that is equal to 1 if herbicide h is appliedon day t or is zero otherwise. Parameter bigM is a large constantthat represents an upper level for variable Mtht,h. Eqs. (6)–(8) con-stitute a big-M formulation, which enforces that if herbicide h is

of herbicide-based weed management. Agr. Syst. (2013), http://dx.doi.org/

Table 4Herbicides parameters. nsh1h and nsh2h are day of beginning and ending of weedsusceptibility to herbicide h (in days); PEAh is the external cost of one application ofherbicide h.

Type Purchase cost($ ha�1)

nsh1h

(day)nsh2h

(day)PEAh

($ ha�1)

Pinoxaden Selective 141.88 10 36 0.15Clodinafop Selective 161.53 10 36 0.16Fenoxaprop Selective 300.14 10 36 0.27Pyroxsulam Selective 114.60 10 36 0.21Diclofop-

methylSelective 158.26 10 27 2.40

Tralkoxydim Selective 111.65 10 27 0.65Glyphosate Non-

selective31.11 1 36 1.94

Paraquat Non-selective

53.48 1 36 2.08

M.V. Lodovichi et al. / Agricultural Systems xxx (2013) xxx–xxx 5

applied on day t (i.e. if yhtht,h = 1), Mtht,h equals the number of seed-lings on the proper growth stage which are eliminated from the sys-tem. Otherwise Mtht,h is set to zero, meaning that no seedlings arecontrolled that day. Notice that the summation in Eqs. (6) and (7)cover the susceptibility period of the weed to each specific herbi-cide denoted by parameters nsh1h and nsh2h (Table 4).

EMtt,h, also defined through a big-M formulation, is equal to Et ifweed seedlings emerged on day t are killed by an application ofherbicide h during their period of susceptibility and is zerootherwise:

EMtt;h P Et � bigMð1� bight;hÞ 8 t; 8 h ð9Þ

EMtt;h 6 Et þ bigMð1� bight;hÞ 8 t; 8 h ð10Þ

EMtt;h 6 bigM bight;h 8 t; 8 h ð11Þ

bight,h is a positive variable that integrates the number of herbicideapplications made during the susceptibility period of weed seed-lings emerged on day t:

bight;h ¼X

tþnsh1h6t16tþnsh2h

yhtht1;h 8 t; 8 h ð12Þ

The total number of individuals controlled on day t is calculatedby integrating the plants controlled by each particular herbicidethat day:

Mt ¼X

h

Mtht;h 8 t ð13Þ

2.3.3. Estimation of weed seed productionWeed seedlings that survive and reach the reproductive stage

by the end of the season will produce new seeds contributing tothe seed bank preservation and therefore to potential infestationproblems in the following years (Cousens and Mortimer, 1995).Specifically for the genus Avena, it has been reported that final seedproduction will depend not only on weed density, but also on theseedlings emergence time (González-Andújar and Fernández-Quintanilla, 1991).

Following González-Andújar and Fernández-Quintanilla (1991),A. fatua emergence was divided into two cohorts in order to differ-entiate early and late emerging individuals. The first cohort in-cludes seedlings emerged until day 181 (i.e. plants born beforeJune 30th) while the second includes the plants emerged thereaf-ter. Day 181 was chosen to divide the two cohorts because a re-duced competitive ability of the weed is assumed from thatperiod on due to competition with the crop.

Seeds produced (S, seeds m�2) at the end of the season wereestimated using the following equation:

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning10.1016/j.agsy.2013.07.006

S ¼ s1D1

1þ b1D1þ s2D2

1þ b2D2ð14Þ

where D1 and D2 are the densities (in plants m�2) of the first and thesecond cohort, respectively while s1, s2, b1 and b2 are fecundityparameters (Table 3).

A proportion of the seed production was considered to be af-fected by various loss sources (during harvest, predation, etc.).Thus, in order to calculate the seed fraction that will effectivelycontribute to the seedbank (seed rain, SR), the following equationwas used:

SR ¼ ð1� lÞS ð15Þ

where l represents the proportion of lost seeds m�2.

2.3.4. Estimation of crop yield loss and final crop yieldAs mentioned above, the model adopts the TDE approach to cal-

culate crop yield loss, in order to account for the impact of weedemergence time on competition. To obtain the daily TDE (TDEt) itwas necessary to consider only those plants that would continuein the system until harvest. For weed seedlings emerged on dayt, Ettt is defined as those individuals that are not killed by any her-bicide application, and is calculated as follows:

Ettt ¼ Et

Xh

EMtt;h 8 t ð16Þ

Ettt represents the daily density incorporated to the system. Thisvariable replaces D in Eq. (4) to calculate the daily TDE:

TDEt ¼ Ettt expð�cRTtÞ 8 t ð17Þ

RTt is the relative time of emergence of seedlings emerged on day twith respect to the crop. For each day on the planning horizon, it iscalculated as:

RTt ¼ Temt � Dec 8 t ð18Þ

Temt is a parameter that represents the date of weed seedling emer-gence on day t, and Dec is the day of crop emergence. Dec is calcu-lated from sowing date (Des) and the time period from sowing tocrop emergence (Tec) as:

Dec ¼ Desþ Tec ð19Þ

The global TDE (TDEtot) represents the total number of weedplants that will be present in the system until crop harvest and thatwill be responsible for crop yield loss. It is then calculated asfollows:

TDEtot ¼X

t

TDEt ð20Þ

This global TDE replaces D in Eq. (1) to estimate the impact thatthese plants have on crop yield. yL is obtained as a percentage ofthe potential yield that the crop could produce:

yL ¼iTDEtot

1þ iTDEtota

ð21Þ

Finally, it is necessary to calculate the final crop yield (y) to esti-mate the profit obtained at the end of the season using Eq. (2):

y ¼ ywf 1� yL

100

� �ð22Þ

2.3.5. Objective functionThe herbicides application planning problem is formulated as

an optimization model aimed at maximizing the economic benefit(B) of the agricultural activity. The proposed objective functionconsiders an income term (Inc) related to the predicted crop yield,a purchase (Cost) and an application cost (Cap), both related to

of herbicide-based weed management. Agr. Syst. (2013), http://dx.doi.org/

0 100 200 3000

50

100200320042007

t (calendar days)

Acc

umul

ated

em

erge

nce

(%)

Fig. 1. Avena fatua emergence patterns from EEA INTA Bordenave (Bordenave,Argentina) analyzed using the operational model. X-axis represents an entire year,from day 1 (January 1st) to day 365 (December 31st).

6 M.V. Lodovichi et al. / Agricultural Systems xxx (2013) xxx–xxx

control operations, and the environmental costs (Ext) of the appliedchemicals:

B ¼ Inc � Cost � Cap� Ext ð23Þ

The gross income at the end of the season depends on both thefinal crop yield (y) and the price of the grain (pc). It is calculated asfollows:

Inc ¼ pc � y ð24Þ

The total purchase cost of the applied herbicides is calculatedfrom the cost of a given application as:

Cost ¼X

h

costhh

Xt

yhtht;h

!ð25Þ

where costhh is the purchase cost in $ ha�1 of herbicide h.Similarly the application cost of the herbicides is calculated

from the cost of each individual application:

Cap ¼ apX

t

Xh

yhtht;h ð26Þ

where ap is the cost (in $ ha�1) of one application of herbicide.Finally, the environmental cost (Ext) associated to herbicide

applications is calculated as a function of the external cost of eachapplication (PEAh) performed by the model:

Ext ¼X

t

Xh

yhtht;hPEAh

!ð27Þ

As already mentioned, the current model was conceived asan operational (i.e. within-season) module intended to be usedas a part of a tactical/strategic planning system which wouldtake into account a longer term decision horizon based onmonitoring the seed population along the years and also con-sidering mechanical and cultural control options in the decisionprocess.

However, in order to consider the fact that the uncontrolledseedlings will produce seeds that eventually would have an impacton the following seasons, complementary studies were undertakenby including an additional term in the objective function. Thispenalization term (Rep) accounts for the future cost that weed seedproduced during the current season might have the following yearand is modeled as:

Rep ¼ p � SR ð28Þ

where SR is the seed rain (Eq. (15)) and p represents a penalty costin $ ha�1 (seed m�2) whose estimation is provided in Section 3.3.

2.3.6. HerbicidesNon-selective herbicides are available to control weeds before

crop sowing, in order to early eliminate individuals with a greatcompetitive advantage. Selective herbicides are available for weedcontrol purposes after the crop’s susceptibility period. Restrictionswere included to avoid spraying operations in periods where thedifferent herbicides cannot be applied. Constraint (29) avoids theapplication of non-selective herbicides after sowing:

yhtht;h ¼ 0 8 t P Des; 8 hns ð29Þ

Constraint (30) prevents the application of selective herbicidesbefore sowing and during crop’s susceptibility period:

yhtht;h ¼ 0 8 t 6 Decþ ns; 8 hs ð30Þ

Eq. (31) avoids the application of a selective herbicide morethan once in the season. This is a ‘‘heuristic’’ constraint to mimica practice intended to mitigate the manifestation of weed resis-tance in the long term and to avoid crop phytotoxicity.

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning10.1016/j.agsy.2013.07.006

Xt

yhtht;h 6 1 8 hs ð31Þ

Finally, constraint (32) avoids the application of selective herbi-cides beyond the period (tc) when the crop has reached a growthstage that does not allow control tasks:X

h

yhtht;h ¼ 0 8 t P tc ð32Þ

The GAMS platform and the solver Dicopt++ (GAMS 2008a,b)were used to program and solve the resulting mixed integer non-linear model.

2.4. Scenario analysis

A. fatua emergence patterns of the semiarid region of Argentinaare difficult to predict mainly due to highly variable environmentalconditions (i.e. precipitations and temperature) and also to specificecological adaptations of the species in relation to the seedbankdormancy dynamics (Chantre et al., 2012). After analyzing twelveyears (1999–2010) of A. fatua emergence data from ExperimentalStation of INTA at Bordenave, Argentina (37�500S; 63�010W), threedifferent seedling emergence patterns were chosen to test the pro-posed model. These patterns were selected according to the timetaken to reach 50% of the total emergence. The chosen scenarioscorrespond to years 2003 (Case 1), 2004 (Case 2) and 2007 (Case3), where 50% of emergence was reached after 145, 215 and 110calendar days, respectively (Fig. 1). The adopted patterns are con-sidered to be representative of contrasting field emergence scenar-ios observed under such environmental conditions. Nevertheless, itshould be stressed that the decision maker is able to feed the pro-posed model with any plausible emergence pattern to generate thecorresponding control plan. A non-dormant seed bank of200 seeds m�2 was adopted for the base case scenario analysis.

The model parameters for the T. aestivum–A. fatua system arereported in Table 3. Parameters related to competition (Eqs. (1)and (4)) and seed production (Eqs. (14) and (15)) were obtainedfrom specific literature (Cousens et al., 1987; González-Andújarand Fernández-Quintanilla, 1991). Site specific agronomic data(emergence patterns, weed free crop yield, day of crop sowingand emergence) were obtained from historical records of INTAand expert knowledge (Table 3). Economic related data was gath-ered from public sources and data for the environmental impactquotient (EIQ) calculation was collected from several data bases(Appendix A). Regarding the estimation of the susceptibility periodto herbicides (nsh1h and nsh2h), wild oat plants phenology wasweekly examined following the Zadoks classification system (Za-doks et al., 1974). Then, thermal-time (in �C day) to reach eachstage was calculated. Using average daily temperatures, the time

of herbicide-based weed management. Agr. Syst. (2013), http://dx.doi.org/

0 100 200 300 4000

10

20

30

40

50

60

70DtTDEtot

t (calendar days)

Plan

ts/m

2

Fig. 2. Case 1: evolution of total weed density (Dt, plants m�2) (solid line) and weeddensity affecting crop yield (TDEtot, plants m�2) (dashed line). Arrows indicate thetime of herbicide applications.

Table 5Results summary.

M.V. Lodovichi et al. / Agricultural Systems xxx (2013) xxx–xxx 7

(in days) to reach each stage was estimated to determine thebounds of the susceptibility period. For graminicides, nsh1h corre-sponds to the day when the plants have 2 leaves, while for non-selective herbicides it refers to the cohort’s emergence day; nsh2h

is the day when plants reach either a 4 leaves stage or beginningof tillering, depending on herbicide h.

Eight chemicals with different active ingredients, commonlyused for A. fatua control in Argentina, were considered in this casestudy. In Table 4, two non-selective pre-sowing herbicides and sixselective post-emergence herbicides are depicted. Each herbicidehas different application and environmental costs and periods ofweed and crop susceptibility. They were all considered as sprayedat label dose recommendations. The details of the Pesticide Envi-ronmental Accounting calculation for each particular herbicideare provided in Appendix A.

From a statistics point of view it is worth mentioning that a typ-ical instance of the model expands 2920 binary variables, 13,518positive variables and 25,204 constraints (equality and inequality)and demands a few CPU minutes in a standard desktop computer.

Case 1(2003)

Case 2(2004)

Case 3(2007)

Final weed density(plants m�2)

61 154 72

TDEtot (plants m�2) 18 3 23Weed seed production

(seeds m�2)443 551 632

Seed rain (seeds m�2) 204 254 291Crop yield loss (%) 11.9 2.4 14.8Crop yield (kg ha�1) 1761.8 1952.6 1703.9Income ($ ha�1) 1321.4 1464.4 1277.9Purchase cost ($ ha�1) 207.9 62.2 93.3Application cost

($ ha�1)66 33 49.5

Externalities ($ ha�1) 6.0 3.9 5.8Benefit ($ ha�1) 1041.4 1365.3 1129.3

2.5. Sensitivity analysis

The model parameters were assumed constant in the scenarioanalysis but most of them have a significant level of uncertainty.The purpose of the sensitivity analysis is to investigate the robust-ness of the base case solution in a neighborhood of the typicalparameters values. Specifically, the seedbank size was disturbedin ±10%, 20% and 25% while the weed susceptibility period to her-bicides was modified in ±10% regarding the base case. The modelwas re-run each time and the most important variables reportedfor comparison purposes. The sensitivity to these parameters is re-ported using the emergence pattern corresponding to year 2003(Case 1) as base case scenario.

Selected herbicidetype: Applicationdays

Glyphosate: 71/111/147, pyroxsulam: 198

Glyphosate:110/146

Glyphosate:79/115/151

0 100 200 300 4000

100

200DtTDEtot

t (calendar days)

Plan

ts/m

2

Fig. 3. Case 2: evolution of total weed density (Dt, plants m�2) (solid line) and weeddensity affecting crop yield (TDEtot, plants m�2) (dashed line). Arrows indicate thetime of herbicide applications.

3. Results and discussion

3.1. Scenario analysis

Optimization results indicate that in Case 1 (Fig. 2), where 50%of wild oat emergence was reached a few days before sowing, themaximum benefit was obtained after three pre-sowing glyphosatetreatments, and one post-emergence application of pyroxsulam.These applications controlled more than half of the seedlingsemerged during the considered planning horizon. Although afterthe last application the final weed density increased, the numberof plants affecting crop yield loss remained constant. Final weeddensity was 61 plants m�2, but only 18 individuals had a signifi-cant impact on final crop yield (Table 5).

In Case 2 (Fig. 3), the model proposed only two glyphosateapplications in crop pre-emergence. These applications were suffi-cient to control the few plants emerged during that period. Becausemost weed seedlings emerged long after sowing, their impact oncrop yield was not significant and it would not be optimal to per-form any post-emergence control action. As observed in Table 5,only 2% of the individuals had a significant impact on crop yield de-spite final weed density after glyphosate applications was154 plants m�2.

Finally, in Case 3 (Fig. 4), where 50% of emergence was reachedlong before sowing, three applications of glyphosate were required.In this case, final weed density was 72 plants m�2 from which23 plants m�2 were responsible for the predicted crop yield loss(Table 5). Although after the last application global TDE increasedconsiderably, those plants were not controlled because the post-emergence herbicide should have been applied during the cropsusceptibility period.

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning10.1016/j.agsy.2013.07.006

By analyzing the studied scenarios it is evident that early emer-gent A. fatua cohorts, which have a large impact on crop yield, re-quire several pre-sowing herbicide applications in all cases. Ifemergence is too early (Case 3), only pre-sowing treatments are re-quired because all potentially competitive weeds are removed atthis stage. If weed emergence is considerably delayed (Case 2),weed seedlings emerging after crop establishment do not have asignificant effect on cereal yield and additional applications arenot required. The most challenging scenario arises when a largeproportion of the weed emergence is overlapped with the crop sus-ceptibility period (Case 1). In this case, some post-emergence

of herbicide-based weed management. Agr. Syst. (2013), http://dx.doi.org/

0 100 200 300 4000

102030405060708090

DtTDEtot

t (calendar days)

Plan

ts/m

2

Fig. 4. Case 3: evolution of total weed density (Dt, plants m�2) (solid line) and weeddensity affecting crop yield (TDEtot, plants m�2) (dashed line). Arrows indicate thetime of herbicide applications.

8 M.V. Lodovichi et al. / Agricultural Systems xxx (2013) xxx–xxx

control action is required to avoid excessive competitive pressureon the crop.

In the absence of control operations, the analyzed emergencepatterns would have led to a great infestation. Considering thatA. fatua is a strong competitor and can reduce crop yield to around100%, the control treatments proposed by the model were capableof reducing crop yield losses to less than 15% in all cases. The envi-ronmental costs of herbicide applications were considered in theobjective function for the three emergence scenarios. In all casesthese values were much lower than the corresponding applicationcosts and therefore had not shown a considerable impact on thechoice of the control strategies.

The performance of more than one application of glyphosateduring the same season might be considered as a non-recommend-able practice because it represents a strong pressure on weed pop-ulations that may lead to increase herbicide resistance rate. Theuse of the alternative non-selective ingredient (i.e. Paraquat) wasnever advised by the model due to its high relative cost with re-spect to glyphosate. In the cases where glyphosate was constrainedto be applied only once along the season, negative benefits were

Table 6Sensitivity analysis (seed bank). Application days are the periods when herbicides are app

Variable Percentage of change

�25% �20% �10% Base

Seed bank(seeds m�2)

150 160 180 200

Final weed density(plants m�2)

45 66 54 61

Weed seedproduction(seeds m�2)

328 938 390 443

Seed rain(seeds m�2)

151 431 179 204

TDEtot(plants m�2)

9.3 23.4 14.7 18.0

Crop yield loss (%) 6.5 14.9 9.9 11.9Crop yield

(kg ha�1)1869.7 1701.7 1801.9 1761

Income ($ ha�1) 1402.3 1276.3 1351.4 1321Purchase cost

($ ha�1)207.9 93.3 207.9 207.

Application cost($ ha�1)

66 49.5 66 66

Externalities($ ha�1)

6.0 5.8 6.0 6.0

Benefit ($ ha�1) 1122.3 1127.6 1071.4 1041Selected herbicide

type:Applicationdays

Glyphosate: 77/114/150,pyroxsulam: 196

Glyphosate:75/115/151

Glyphosate: 77/113/149,pyroxsulam: 196

Glyp111/pyro

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning10.1016/j.agsy.2013.07.006

obtained due to an unfavorable balance between control costsand cereal yields (results not shown). Despite its inadequacy froma management perspective, it should be mentioned that in the re-gion under study, it is a common practice to repeat glyphosateapplications during fallow in order to control many problematicgramineous and broad-leaved weeds.

The advice given by the model of whether to apply or not thegraminicide is of great practical importance. This decision is oneof the most difficult to make because each herbicide applicationis expensive, and it is of practical interest for the producer or agro-nomic advisor to know if it is worth to implement it.

Surviving plants did not have a significant impact on crop yieldat the current season, but their seed production might affect theactivities of the following year. In Case 1 seed rain from the surviv-ing plants did not considerably affect the initial seedbank size. InCases 2 and 3, on the other hand, the seed rain produced by theremaining plants contributed to the enlargement of the initialseedbank size with respect to that of the current year (27% and45.5% respectively).

The fact that in the three cases the seedbank did not suffer a sizereduction means that the following year a more intense manage-ment strategy might be necessary in order to control the potentialemergence. A program based only on the use of herbicides wouldlead not only to a large environmental impact but also to an in-creased risk of development of resistant weed populations. Thus,complementary management options such as crop rotations (i.e.a summer crop, a permanent pasture, etc.) or a fallow year wouldcontribute to control wild oat infestations in a more sustainableway. Such control options should be analyzed at a strategic deci-sion making level.

3.2. Sensitivity analysis

In Table 6 the sensitivity of most relevant variables with respectto the seed bank size is presented. For increasing number of seedsin the seed bank it can be observed that the application strategy

lied.

case +10% +20% +25%

220 240 250

66 72 76

456 471 513

210 217 236

18.0 17.4 25.0

11.9 11.5 15.8.8 1762.1 1769. 2 1684.1

.4 1321.6 1326. 9 1263.19 207.9 207.9 207.9

66 66 66

6.0 6.0 6.0

.4 1041.6 1046.9 983.1hosate: 71/147,xsulam: 198

Glyphosate: 78/114/150,pyroxsulam: 197

Glyphosate: 75/115/151,pyroxsulam: 197

Glyphosate: 79/115/151,pyroxsulam: 196

of herbicide-based weed management. Agr. Syst. (2013), http://dx.doi.org/

Table 7Sensitivity analysis (weed susceptibility period).

Variable Percentage of change

�10% Base case 10%

Final weed density(plants m�2)

83 61 58

TDEtot (plants m�2) 33.0 18.0 6.3Weed seed

production(seeds m�2)

1123 443 335

Seed rain(seeds m�2)

517 204 154

Crop yield loss (%) 19.8 11.9 4.5Crop yield (kg ha�1) 1603.1 1761.8 1909.2Income ($ ha�1) 1202.3 1321.4 1431.9Purchase cost

($ ha�1)93.3 207.9 207.9

Application cost($ ha�1)

49.5 66 66

Externalities($ ha�1)

5.8 6.0 6.0

Benefit ($ ha�1) 1053.7 1041.4 1151.9Selected herbicide

type: Applicationperiods

Glyphosate:89/120/151

Glyphosate: 71/111/147,pyroxsulam: 198

Glyphosate: 70/110/150,pyroxsulam: 196

Table 8Control costs used to calculate parameter p. SB200 and SB9 are seedbanks with 200 and9 seeds m�2 respectively.

Case 1 (2003) Case 2 (2004) Case 3 (2007)

SB200 SB9 SB200 SB9 SB200 SB9

Purchase cost ($ ha�1) 207.9 62.2 62.2 31.1 93.3 62.2Application cost ($ ha�1) 66 33 33 16.5 49.5 33External cost ($ ha�1) 6.0 4.3 3.9 2.1 5.8 4.3Total cost ($ ha�1) 279.9 99.5 99.1 49.7 148.6 99.5p Value ($ m2 ha�1 seed�1) 0.94 0.26 0.26

Table 9Results summary (with penalty).

Case 1(2003)

Case 2(2004)

Case 3(2007)

Final weed density(plants m�2)

61 48 72

TDEtot (plants m�2) 18 3 23Weed seed

production(seeds m�2)

443 371 632

Seed rain(seeds m�2)

204 171 291

Crop yield loss (%) 11.9 1.9 14.8Crop yield (kg ha�1) 1761.8 1960.8 1703.9Income ($ ha�1) 1321.36 1470.6 1277.9Purchase cost

($ ha�1)207.9 176.8 93.3

Application cost($ ha�1)

66 49.5 49.5

Externalities ($ ha�1) 6.0 4.1 5.8Weed seed penalty

($ ha�1)99.9 83.7 107.2

Benefit ($ ha�1) 941.5 1156.6 986.8Selected herbicide

type: Applicationdays

Glyphosate: 78/114/150, pyroxsulam:198

Glyphosate: 112/149, pyroxsulam:239

Glyphosate:79/115/151

M.V. Lodovichi et al. / Agricultural Systems xxx (2013) xxx–xxx 9

did not change significantly, since three pre-sowing applications ofglyphosate and one post-emergence application of pyroxsulamtook place approximately in the same periods for all cases. Inter-estingly, larger benefits are observed for larger seed banks (+10%and +20%) with respect to the base case only due to the shifts inthe periods of application. For the 25% increased seed bank, theapplication strategy could not compensate the weed competitivepressure and a reduced crop yield was obtained with respect tothe base case.

As expected, for decreasing seed banks, larger benefits with re-spect to the base case were obtained in all scenarios. For the �10%and �25%, the application program is the same as in the base case,with minor variations in the glyphosate application periods. How-ever, in the �20% case, only the three pre-sowing glyphosate appli-cations were required, with no post-emergence intervention.Although a larger crop yield loss took place in this situation(14.9%), significantly reduced control costs compensated the in-come decrease, producing a larger benefit than in the base case.

Regarding seed production, increases in seedbank size led to in-creased seed rains in all cases because more weed plants remainuncontrolled under the same application program. For the caseswhere the seedbank was reduced and the application programdid not change with respect to that of the base case (i.e. �10%and �25% cases), the seed rain was also reduced compared to theoriginal seedbank. However, in the �20% case, where one less her-bicide application was performed, the larger number of uncon-trolled plants that survived for reproduction significantlyincreased the seedbank for the following year (111%).

In Table 7 the sensitivity of the solution with respect to the sus-ceptibility period of the weed to the herbicides is presented. The

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning10.1016/j.agsy.2013.07.006

susceptibility to all herbicides was modified simultaneously in or-der to simulate environmental conditions that enlarges and re-duces the control period of the herbicides. For example, in the+10% case, nsh1h was reduced in 10% and nsh2h incremented in10% enlarging the effectiveness periods of the herbicides. In thiscase, the control solution remains the same as in the base case(three pre-sowing and one post-emergence treatment) with someshifts in the applications. However, the enlarged control action ofthe herbicides allowed a significant reduction in TDEtot (64.83%)which produced a larger cereal yield with the consequent benefits.

A reduced herbicide efficiency (�10% case) provided an optimaltreatment with only three pre-sowing applications and no post-emergence control. The application times of the first two controlswere quite delayed regarding the base case in order to better con-trol the emergent weed. Although the crop yield loss increasedregarding the base case, the reduced costs compensated for the re-duced benefits in the economic equation.

With respect to seed production, a larger weed susceptibilityperiod than the one of the base case reduced weed density in thefield, thus reducing the seed rain. In the �10% case, on the otherhand, the less aggressive strategy with respect to the base case(no post-emergence application) led to a large seed rain which in-creased in 153% the original seed bank.

By analyzing the sensitivity study it can be concluded that thesolutions are quite robust in the sense that basically the sametreatment is obtained in most cases (three pre-sowing and onepost-emergence applications). The major variations are found inthe application timing. By adequate shifts in the application peri-ods, the model is able to compensate for unfavorable situations(i.e. increased seed banks) or to exploit favorable conditions (i.e.enlarged susceptibility periods) without changing the overall her-bicides combination. In the cases where post-emergence applica-tions were not required (20% seed bank reduction and 10%susceptibility period reduction) significant crop yield losses werecompensated in both cases by a reduction of costs due to one lesschemical application, at the expense of large seed rains with poten-tial consequences in future seasons.

3.3. Scenario analysis penalizing weed seed production

Surviving plants that might not significantly impact on cropyield could have important consequences on a long-term time

of herbicide-based weed management. Agr. Syst. (2013), http://dx.doi.org/

0 100 200 300 4000

10

20

30

40

50

60

70DtTDEtot

t (calendar days)

Plan

ts/m

2

Fig. 5. Case 1: evolution of total weed density (Dt, plants m�2) (solid line) and weeddensity affecting crop yield (TDEtot, plants m�2) (dashed line), considering a penaltyin the objective function for each extra seed produced. Arrows indicate the time ofherbicide applications.

0 100 200 300 4000

50

100

150DtTDEtot

t (calendar days)

Plan

ts/m

2

Fig. 6. Case 2: evolution of total weed density (Dt, plants m�2) (solid line) and weeddensity affecting crop yield (TDEtot, plants m�2) (dashed line), considering a penaltyin the objective function for each extra seed produced. Arrows indicate the time ofherbicide applications.

0 100 200 300 4000

102030405060708090

DtTDEtot

t (calendar days)

Plan

ts/m

2

Fig. 7. Case 3: evolution of total weed density (Dt, plants m�2) (solid line) and weeddensity affecting crop yield (TDEtot, plants m�2) (dashed line), considering a penaltyin the objective function for each extra seed produced. Arrows indicate the time ofherbicide applications.

10 M.V. Lodovichi et al. / Agricultural Systems xxx (2013) xxx–xxx

horizon because they produce seeds that will be incorporated tothe soil seedbank leading to potential infestation problems in thefollowing seasons. In fact, the results of the previous sections sug-gest that the plants that remained in the system produced a con-siderable amount of seed. Such seeds have to be considered in atactical/strategic decision support system which monitors the pop-ulation dynamics along the seasons and considers every availablecontrol option together with chemical use.

An additional study is provided in this section to investigate thepotential effects of the reproduction of surviving plants. The pro-posed study is based on the penalization of the seed rain according

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning10.1016/j.agsy.2013.07.006

to Eq. (28). This penalization term is intended to quantify the po-tential future infestation costs through parameter p.

In this contribution, parameter p was obtained for each weedemergence pattern as the slope of the linear combination betweenthe control costs (i.e. the sum of purchase, application and externalcosts) corresponding to two extreme initial seedbank sizes (9 and200 seeds m�2). Specifically:

p ¼ C200 � C9

SB200 � SB9ð33Þ

where C200 and C9 are total control costs when the seedbank has200 and 9 seeds m�2, respectively, and SB200 and SB9 are the seed-bank sizes. Parameter p was calculated for each one of the threeemergence patterns and then averaged out to be used in Eq. (28).The calculation details are presented in Table 8.

The three scenarios reported in Section 3.1 were also studied byincluding the penalization term due to weed seed production. Re-sults are summarized in Table 9 and Figs. 5–7.

In Cases 1 (Fig. 5) and 3 (Fig. 7), the selected control strategieswere the same as in the no penalty case, although some shifts inapplication days were observed (Table 9). The benefits were lowerthan in the no penalization scenario due to the extra cost assignedto seed production (9.6% and 12.6% respectively).

In case 2, on the other hand, significant variations regarding theno penalty counterpart were observed. An additional post-emer-gence application of pyroxsulam was recommended (Fig. 6). Weedseed produced was considerably reduced compared with the nopenalty case (Table 9). With this new strategy, the final weed den-sity was reduced from 154 to 48 plants m�2 and despite the factthat control costs increased, the final income was still positive be-cause the increased cereal yield compensated the additionalapplication.

In practice, one post-emergence herbicide application is a rea-sonable strategy to reduce crop yield loss in the current seasonand/or to reduce the impact of weed seed production in the follow-ing. It should be stressed that this model is intended to operatewithin an integrated weed management framework which ad-dresses the medium/long term decisions considering not onlychemical control, but also preventive, mechanical, biological andcultural strategies. In this scope, probably other management pro-cedure, as for example crop rotation or mechanical control, shouldbe recommended for the following season instead of an additionalherbicide application in case 2.

4. Conclusions and future work

The model proposed in this work automates the calculation ofthe optimal application times of herbicides within a growing sea-son. Optimization depends on the estimated weed emergence pat-tern, which strongly depends on soil microclimatic conditions andthe dormancy level of seedbank associated to seasonal variations ofsoil temperature (Forcella et al., 2000). The emergence pattern wastreated as a single parameter in the model in order to compriseboth, the biological and the climatic components involved in weedemergence. If available, sub-models that relate weed emergencewith weather forecasts can be used. Many of these have beendeveloped in the last years for different systems (Forcella et al.,2000; Chantre et al., 2012, in press).

One of the most challenging aspects was the calculation of cropyield loss according to weed density. Because weed seedlings thatemerge earlier are more influential in competition, in this workthey were weighted according to their emergence time. Therefore,although the final weed density is over-estimated by the model be-cause the fed emergence patterns consider that seedlings keepemerging after the crop canopy closure, the competitive influence

of herbicide-based weed management. Agr. Syst. (2013), http://dx.doi.org/

M.V. Lodovichi et al. / Agricultural Systems xxx (2013) xxx–xxx 11

of these late emerging plants does not have a significant effect oncereal yield. However, in order to make a more realistic calculation,both, age and permanence in the system should be considered.Moreover, the competition for nitrogen, light and water might beaddressed through the mechanistic modeling of the crop–weedinteractions (Kropff and Van Laar, 1993).

If plant reproduction is not taken into account during the withinseason analysis, it is possible that an optimal control strategyleaves uncontrolled weed plants that eventually will produce seedcontributing to the seedbank preservation and therefore to poten-tial infestation problems in the following seasons.

In order to deal with this issue, seed production was penalizedas an additional cost in the planning objective function. The inclu-sion of a penalization term due to seed production allows account-ing for possible future expenses stemming from such seed. In thisway, the model can advise for additional (preventive) herbicideapplications that may not be economically optimal from the pointof view of the current season but make sense in the medium term.However, the long term decisions are to be addressed from a morestrategic approach.

In other words, the developed model is operational in nature,meaning that only short term (seasonal) decisions are considered.Moreover, only chemical control options at the recommended labeldoses were included in the present version. There are other controlmethods that should be taken into account from a strategic point ofview, summarized as preventive, cultural, mechanical and biologi-cal procedures. The importance of integrated weed managementplanning has been largely recognized in order to account for thelong-term effects of crop rotations or other cultural controls onweed infestation levels and manifestation of chemical resistantbiotypes (Pannell et al., 2004; Parsons et al., 2009). In this sensethe proposed model can be considered as the seasonal module ofthe chemical control within a strategic planning system.

It was also recognized in the development of the DSS that prac-tically every model parameter presents a significant uncertainty,specifically those that somehow depend on climatic conditions.Sensitivity analysis on most influential parameters revealed inter-esting behaviors, suggesting that uncertainty should be explicitlyhandled in real applications. A practical solution could be to runthe model within a model predictive control framework in orderto identify the short term optimal solution with the available

Table A1EIQ calculation.

Active ingredient Pinoxaden Clodinafop Fenoxaprop Pyroxsulam Diclometh

EIQe per categoryApplicator effects 5 15 5 5 15Picker effects 3 9 3 3 9Consumer effects 2 6 2 2 6Ground water 3 1 1 1 1Aquatic effects 3 25 25 3 9Bird effects 6 6 6 6 6Bee effects 9 9 9 9 9Beneficial insects

effects15 15 15 15 45

EIQe 15.33 28.67 22 14.67 33.3% a.i. in formulation 5 8 6.9 4.5 28.4Rate (kg or l

formulation per ha)0.6 0.36 0.85 0.4 2

EIQe field use rating 0.46 0.83 1.29 0.26 18.9

a Acid equivalent concentration in formulation.b In pinoxaden formulation.c In clodinafop formulation.d In pyroxsulam formulation.e Environmental impact quotient.

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning10.1016/j.agsy.2013.07.006

weather forecast and recalculate a new solution as a new forecastsbecome available, taking into account the already implementedcontrol actions (Ogunnaike and Ray, 1994).

Finally, the Pesticide Environmental Accounting methodologywas chosen among the environmental impact evaluation ap-proaches because it allowed straightforwardly including the envi-ronmental component as an externality in the model objectivefunction to account for the environmental impact of the herbicidesapplication. This inclusion did not produce a significant impact onthe model output since external costs per application of any of theherbicides considered is much lower than application costs. How-ever, the explicit inclusion of an environmental component in eco-nomic terms is practical to quantify the effect of the differentavailable chemical options and to highlight the environmental con-cern during the agricultural decision making process.

If alternative environmental impact indicators, not formulatedin economic terms, are to be analyzed, a multi-objective approachshould be adopted to study the trade-off between maximizing theeconomic benefit and minimizing the environmental impact.

Acknowledgements

This work was partially supported by: Consejo Nacional deInvestigaciones Científicas y Técnicas, Agencia Nacional de Promo-ción Científica y Técnica, Universidad Nacional del Sur (Argentina)and Instituto Nacional de Tecnología Agropecuaria of Argentina.We are also grateful to Eng. Jorge Irigoyen (in memoriam) for ex-pert advice and fruitful discussions. We also want to thank twoanonymous reviewers for their helpful comments.

Appendix A

In Table A1 the Environmental Impact Quotient (EIQ) for eachherbicide/category is reported. Data from several sources wereused to calculate the EIQs of the herbicides considered (CASAFE,2007; EXTOXNET; IPM center; US EPA Pesticide Fact Sheets). Thecomponent of each category is calculated as follows (Kovachet al., 1992):

� Applicator effects: (DT.5).C.� Picker effects: (DT.P).C.

fopyl

Tralkoxydim Glyphosate Paraquat Cloquintocetmexyl

Metsulfuronmethyl

15 5 15 5 59 3 9 3 36 3 4 2 41 1 1 1 315 3 1 1 36 9 12 6 129 9 9 9 915 15 45 15 15

3 25.33 16 32 14 1880 36a 27.6 1.25b–2c–9d 600.2 1.5 2 0.60b–0.36c–

0.40d0.0067

3 4.05 8.64 17.66 0.11b–0.10c–0.50d

0.07

of herbicide-based weed management. Agr. Syst. (2013), http://dx.doi.org/

Table A2EIQ variables.

Symbol Name

DT Dermal toxicityC Chronic toxicityP Plant surface residue half-lifeS Soil residue half-lifeSY Pesticide mode of actionL Leaching potentialF Fish toxicityR Surface loss potentialD Bird toxicityZ Bee toxicityB Beneficial arthropod toxicity

Table A3Quotient classification for each EIQ category.

EIQ categories Low range(0.5)

Medium range(1)

High range(1.5)

Applicator effects 5 6 EIQ < 25 25 6 EIQ < 85 85 6 EIQ 6 125Picker effects 1 6 EIQ < 14 14 6 EIQ < 76 76 6 EIQ 6 125Consumer effects 1 6 EIQ < 14 14 6 EIQ < 76 76 6 EIQ 6 125Ground water 1 6 EIQ < 2 2 6 EIQ < 4 4 6 EIQ 6 5Aquatic effects 1 6 EIQ < 5 5 6 EIQ < 17 17 6 EIQ 6 25Bird effects 3 6 EIQ < 15 15 6 EIQ < 51 51 6 EIQ 6 75Bee effects 3 6 EIQ < 15 15 6 EIQ < 51 51 6 EIQ 6 75Beneficial insects

effects5 6 EIQ < 25 25 6 EIQ < 85 85 6 EIQ 6 125

The numbers between brackets are the weights applied to each range.

12 M.V. Lodovichi et al. / Agricultural Systems xxx (2013) xxx–xxx

� Consumer effects: C.((S + P)/2).SY.� Ground water: L.� Aquatic effects: F.R.� Bird effects: D.((S + P)/2).3.� Bee effects: Z.P.3.� Beneficial insects effect: B.P.5.

The involved variables (Table A2), take values 1, 3 or 5 if theireffects are small, medium or large, respectively. Following, aweight was assigned to each category (Table A3), according tothe EIQ value (Leach and Mumford, 2008). Then, the average perhectare cost (in Euros kg�1 of active ingredient) of each categorywas multiplied by the field rate (in kg active ingredient ha�1) ofeach herbicide and by the assigned weight to obtain an estimatedexternal cost in Euros ha�1. Finally, this amount was converted to

Table A4Estimated field use external costs of eight herbicides included in the model.

Activeingredient

Pinoxaden + cloquintocetmexyl

Clodinafop + cloquintocetmexyl

Fenoxaprop Pyrme

Per hectare cost ($ARS)Applicator

effect0.01 0.01 0.02 0.0

Picker effect 0.01 0.01 0.02 0.0Consumer

effect0.06 0.06 0.09 0.1

Ground water 0.03 0.01 0.02 0.0Aquatic effects 0.02 0.04 0.08 0.0Birds effects 0.01 0.01 0.01 0.0Bee effects 0.01 0.01 0.01 0.0Beneficial

insectseffect

0.01 0.01 0.01 0.0

Total ($ARS) 0.15 0.16 0.26 0.2

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning10.1016/j.agsy.2013.07.006

Argentinean currency and affected by the proportional PesticideEnvironmental Accounting to reference GDP (14,41%) to obtainthe external cost of each application (Table A4).

References

Berti, A., Dunan, C., Sattin, M., Zanin, G., Westra, P., 1996. A new approach todetermine when to control weeds. Weed Sci. 44, 496–503.

Berti, A., Zanin, G., 1997. GESTINF: a decision support model for post-emergenceweed management in soybean (Glycine max (L.) Merr.). Crop Prot. 16, 109–116.

Berti, A., Bravin, F., Zanin, G., 2003. Application of decision-support software forpostemergence weed control. Weed Sci. 52, 618–627.

CASAFE, 2007. Guía de productos fitosanitarios. Tomo II. Generalidades y productospara la República Argentina. Cámara Argentina de Sanidad Agropecuaria yFertilizantes (CASAFE), Argentina.

Chantre, G., Blanco, A.M., Lodovichi, M.V., Bandoni, J.A., Sabbatini, M.R., Vigna, M.,López, R., Gigón, R., 2012. Modeling Avena fatua seedling emergence dynamics:an artificial neural network approach. Comput. Electron. Agr. 88, 95–102.

Chantre, G.R., Blanco, A.M., Forcella, F., Van Acker, R.C., Sabbatini, M.R., Gonzalez-Andujar, J.L., 2013. A comparative study between nonlinear regression andartificial neural network approaches for modeling wild oat (Avena fatua) fieldemergence. J. Agr. Sci., in press. http://dx.doi.org/10.1017/S0021859612001098.

Colbach, N., Chauvel, B., Gauvrit, C., Munier-Jolain, N.M., 2007. Construction andevaluation of ALOMYSYS modelling the effects of cropping systems on theblackgrass life-cycle: from seedling to seed production. Ecol. Model. 20I, 283–300.

Cousens, R., 1985. A simple model relating yield loss to weed density. Ann. Appl.Biol. 107, 239–252.

Cousens, R., Doyle, C.J., Wilson, B.J., Cussans, G.W., 1986. Modelling the economics ofcontrolling Avena fatua in winter wheat. Pest. Sci. 17, 1–12.

Cousens, R., Brain, P., O’Donovan, J.T., O’Sullivan, P.A., 1987. The use of biologicallyrealistic equations to describe the effects of weed density and relative time ofemergence on crop yield. Weed Sci. 35, 720–725.

Cousens, R., Mortimer, M., 1995. Dynamics of Weed Populations. CambridgeUniversity Press, United Kingdom.

De Buck, A.J., Schoorlemmer, H.B., Wossink, G.A.A., Janssens, S.R.M., 1999. Risks ofpost-emergence weed control strategies in sugar beet: development andapplication of a bio-economic model. Agr. Syst. 59, 283–299.

Doyle, C.J., Cousens, R., Moss, S.R., 1986. A model of the economics of controllingAlopecurus myosuroides Huds. in winter wheat. Crop Prot. 5, 143–150.

EXTOXNET. <http://pmep.cce.cornell.edu/profiles/extoxnet/> (accessed December2012).

Falconer, K., Hodge, I., 2001. Pesticide taxation and multi-objective policy making:farm modeling to evaluate profit/environment trade-offs. Ecol. Econ. 36, 263–279.

Forcella, F., Benech-Arnold, R.L., Sanchez, R., Ghersa, C.M., 2000. Modeling seedlingemergence. Field Crop Res. 67, 123–139.

GAMS, 2008a. A Users’ Guide. GAMS Development Corporation.GAMS, 2008b. The Solvers Manual. GAMS Development Corporation.González-Andújar, J.L., Fernández-Quintanilla, C., 1991. Modelling the population

dynamics of Avena sterilis under dry-land cereal cropping systems. J. Appl. Ecol.28, 16–27.

González-Andújar, J.L., Fernández-Quintanilla, C., 2004. Modelling the populationdynamics of annual ryegrass (Lolium rigidum) under various weed managementsystems. Crop Prot. 23, 723–729.

IPM Center. <http://www.ipmcenters.org/ecotox/> (accessed December 2012).Kovach, J., Petzold, C., Degnil, J., Tette, J., 1992. A method to measure the

environmental impact of pesticides. NY Food Life Sci. Bull. 139, 1–8.Kropff, M.J., van Laar, H.H., 1993. Modelling Crop–Weed Interactions. CAB

International, United Kingdom.

oxsulam + cloquintocetxyl + metsulfuron methyl

Diclofopmethyl

Tralkoxydim Glyphosate Paraquat

2 0.20 0.06 0.19 0.20

2 0.14 0.04 0.14 0.140 0.94 0.27 0.90 0.92

3 0.23 0.06 0.22 0.223 0.52 0.15 0.25 0.251 0.10 0.03 0.09 0.101 0.07 0.02 0.07 0.071 0.2 0.03 0.09 0.19

3 2.4 0.66 1.95 2.09

of herbicide-based weed management. Agr. Syst. (2013), http://dx.doi.org/

M.V. Lodovichi et al. / Agricultural Systems xxx (2013) xxx–xxx 13

Leach, A.W., Mumford, J.D., 2008. Pesticide environmental accounting: a method forassessing the external costs of individual pesticide applications. Environ. Pollut.151, 139–147.

Leach, A.W., Mumford, J.D., 2011. Pesticide environmental accounting: a decisionmaking tool estimating external costs of pesticides. J. Consum. Prot. Food Saf. 6(Suppl. 1), S21–S26.

Mullen, J.D., Taylor, D.B., Fofana, M., Kebe, D., 2003. Integrating long-run biologicaland economic considerations into Striga management programs. Agr. Syst. 76,787–795.

Ogunnaike, B., Ray, H., 1994. Process Dynamics, Modeling, and Control. OxfordUniversity Press, New York.

Pannell, D.J., Stewart, V., Bennet, A., Monjardino, M., Schmidt, C., Powles, S.B., 2004.RIM: a bioeconomic model for integrated weed management of Lolium rigidumin Western Australia. Agr. Syst. 79, 305–325.

Parsons, D.J., Benjamin, L.R., Clarke, J., Ginsburg, D., Mayes, A., Milne, A.E., Wilkinson,D.J., 2009. Weed manager – a model-based decision support system for weedmanagement in arable crops. Comput. Electron. Agr. 65, 155–167.

Pretty, J.N., Brett, C., Gee, D., Hine, R.E., Mason, C.F., Morison, J.I.L., Raven, H.,Rayment, M.D., van der Bijl, G., 2000. An assessment of the total external costsof UK agriculture. Agr. Syst. 65, 113–136.

Please cite this article in press as: Lodovichi, M.V., et al. Operational planning10.1016/j.agsy.2013.07.006

Pretty, J., Brett, C., Gee, D., Hine, R., Mason, C., Morison, J., Rayment, M., van der Bijl,G., Dobbs, T., 2001. Policy challenges and priorities for internalizing theexternalities of modern agriculture. J. Environ. Plan. Man. 44, 263–283.

Rydahl, P., 2004. A Danish decision support system for integrated management ofweeds. Asp. Appl. Biol. 72, 43–53.

Sells, J.E., 1995. Optimizing weed management using stochastic dynamicprogramming to take account of uncertain herbicide performance. Agr. Syst.48, 271–296.

Torra, J., Cirujeda, A., Recasens, J., Taberner, A., Powles, S.B., 2010. PIM (PoppyIntegrated Management): a bio-economic decision support model for themanagement of Papaver rhoeas in rain-fed cropping systems. Weed Res. 50,127–157.

US EPA Pesticide fact sheets. <http://www.epa.gov/opp00001/factsheets/>(accessed December 2012).

Wiles, L.J., King, R.P., Sweizer, E.E., Lybecker, D.W., Swinton, S.M., 1996. GWM:general weed management model. Agr. Syst. 50, 355–376.

Zadoks, J.C., Chang, T.T., Konzak, C.F., 1974. A decimal code for the growth stages ofcereals. Weed Res. 14, 415–421.

of herbicide-based weed management. Agr. Syst. (2013), http://dx.doi.org/